--- title: "Auto transformer merits and Cu saving" subject: "Electrical Machines" chapter: 2 key: "semester_4/electrical_machines:autotransformer-merits-copper-saving" source: https://www.bctengineer.com/q/semester_4/electrical_machines/autotransformer-merits-copper-saving site: BCT Engineering --- # Auto transformer merits and Cu saving Electrical Machines · Chapter 2: Transformer - Asked in: 2078 Chaitra, 2+6 marks - Video: [15 Copper Saving in Aurotransformer Compare with Two Winding Transformer - Derivation and Equation](https://www.youtube.com/watch?v=ZlHx1DKC5ME) — SP Engg. ACADEMY - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/autotransformer-merits-copper-saving - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2 ## Question What is an auto transformer? State its merits and demerits over a two winding transformer. Derive an expression of cu-saving in auto transformer. ## Short answer An auto transformer has a single winding, part common to primary and secondary. Merits: less copper (saving fraction K), smaller size, higher efficiency and better regulation. Demerits: no isolation, high short-circuit current, uneconomical for large ratios. Copper saving = K × W_two-winding, derived from ampere‑turn analysis of winding sections. ## Answer An **auto transformer** is a transformer with only one winding, part of which is common to both the primary and the secondary circuits. Power is transferred partly by conduction (the electrical connection) and partly by induction. ```text I1 I2 o--->---+ +---<--- o | | | N1-N2 | load +----------+---o | N2 | o-------+----------+---o ``` #### Merits over a two-winding transformer 1. Less copper is needed (the saving is a fraction $K$, derived below), so it is cheaper and lighter. 2. Smaller size and lower weight for the same rating, since the core is also smaller. 3. Lower copper and core losses, so higher efficiency. 4. Better voltage regulation, as the leakage reactance and resistance are lower. 5. Continuously variable output is possible with a sliding tap. #### Demerits 1. There is no electrical isolation between primary and secondary. A fault (for example an open circuit in the common winding) can put the full HV-side voltage on the LV side, which is dangerous to the user and the equipment. 2. The short-circuit current is high because of the low internal impedance. 3. It is not economical when the ratio is far from 1 (for example 10:1). 4. For three-phase units the neutral must be solidly earthed, and special protection is needed. #### Copper saving Let $K = \dfrac{N_2}{N_1} = \dfrac{V_2}{V_1} = \dfrac{I_1}{I_2} < 1$. Section AB (of $N_1 - N_2$ turns) carries $I_1$ and section BC (of $N_2$ turns) carries $(I_2 - I_1)$. Copper weight is proportional to the ampere-turns of each section. For the two-winding transformer: $W_{2w} \propto N_1I_1 + N_2I_2 = 2N_1I_1$. For the autotransformer (using $N_2I_2 = N_1I_1$ and $N_2I_1 = KN_1I_1$): $$ \begin{aligned} W_{auto} &\propto (N_1 - N_2)I_1 + N_2(I_2 - I_1) \\ &= N_1I_1 - N_2I_1 + N_2I_2 - N_2I_1 \\ &= 2N_1I_1 - 2N_2I_1 = 2N_1I_1(1 - K) \end{aligned} $$ $$ \frac{W_{auto}}{W_{2w}} = 1 - K,\qquad \boxed{\text{Cu saving} = K\,W_{2w}} $$ For example, with $K = 0.8$ the autotransformer needs only 20% of the copper of an equivalent two-winding transformer, a saving of 80%. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines an autotransformer? A. Two windings on one core with a tapping B. One winding, part of which is common to primary and secondary C. A winding with no core D. Two windings connected in series opposing Answer: B. The single winding is shared, so power passes by both conduction and induction. (Key point: Definition) 2. Which is a demerit of an autotransformer? A. No electrical isolation between primary and secondary B. Poorer voltage regulation C. Larger size for the same rating D. Lower efficiency Answer: A. A HV-side fault can reach the LV side because the windings are electrically connected. (Key point: Main demerit) 3. How is power transferred in an autotransformer? A. Entirely by induction B. Entirely by conduction C. Partly by conduction and partly by induction D. Only by mutual flux in the common part Answer: C. Only the fraction (1 - K) is transformed by induction; the rest passes directly. (Key point: Power transfer) 4. What is the copper saving of an autotransformer relative to a two-winding transformer? A. K times the copper of the two-winding transformer B. (1 - K) times that copper C. 2K times that copper D. K^2 times that copper Answer: A. W_2w - W_auto = 2N1I1 - 2N1I1(1-K) = K W_2w. (Key point: Cu saving result) ## Related in Electrical Machines - [Copper saving in auto-transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aautotransformer-copper-saving) — Electrical Machines, chapter 2 - [Copper saving in auto transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aautotransformer-copper-saving) — Electrical Machines I, chapter 2 - [CT secondary open; auto transformer economy](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Act-open-autotransformer-economical) — Electrical Machines, chapter 2 - [Transformer losses and efficiency expression](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atransformer-losses-efficiency-expression) — Electrical Machines, chapter 2 - [Reluctances and air gap flux of two-winding core](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atwo-winding-core-reluctance-airgap-flux) — Electrical Machines I, chapter 1 ## Related in other subjects - [Autotransformer working and Cu saving](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aautotransformer-principle-cu-saving) — Electrical Machine, chapter 2 - [Static differential relay for two-winding transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-differential-two-winding) — Switchgear and Protection, chapter 8 - [Merits and demerits of interconnected system](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Ainterconnection-merits-demerits) — Power System Analysis II, chapter 1, asked 3× - [Average rainfall methods with merits and demerits](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aavg-rainfall-methods-merits) — Engineering Hydrology, chapter 2, asked 2×